2.3.50 Problems 4901 to 5000

Table 2.643: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
4901	24658	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=21 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.325
4902	24674	\begin{align*} y^{\prime \prime }-y&=x^{4} \\ \end{align*}	✓	✓	✓	✓	0.325
4903	26119	\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=x +x \,{\mathrm e}^{x}+x \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.325
4904	429	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.326
4905	465	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.326
4906	1072	\begin{align*} \left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.326
4907	1362	\begin{align*} y^{\prime \prime }-y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.326
4908	1740	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (0\right ) &= k_{0} \\ y^{\prime }\left (0\right ) &= k_{1} \\ \end{align*}	✓	✓	✓	✓	0.326
4909	2377	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
4910	4091	\begin{align*} y^{\prime }&=1-x^{5}+\sqrt {x} \\ \end{align*}	✓	✓	✓	✓	0.326
4911	5998	\begin{align*} -\left (n \left (n +1\right )-a^{2} x^{2}\right ) y+2 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
4912	9068	\begin{align*} y^{\prime }&=\arcsin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.326
4913	9218	\begin{align*} 2 y^{\prime \prime }+2 y^{\prime }+3 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
4914	10510	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +6 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.326
4915	16053	\(\left [\begin {array}{cc} 0 & 1 \\ 2 & 0 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.326
4916	16262	\begin{align*} y^{\prime }-{\mathrm e}^{2 x}&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
4917	17625	\begin{align*} x^{3} y^{\prime \prime \prime }+22 x^{2} y^{\prime \prime }+124 y^{\prime } x +140 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
4918	18225	\begin{align*} y^{\prime \prime }-y&=x +\sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.326
4919	18903	\begin{align*} y^{\prime \prime }+w^{2} y&=\cos \left (2 t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.326
4920	19477	\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ y \left (1\right ) &= {\mathrm e}^{2} \\ y^{\prime }\left (1\right ) &= 3 \,{\mathrm e}^{2} \\ \end{align*}	✓	✓	✓	✓	0.326
4921	19509	\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.326
4922	19855	\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=x^{3} \\ \end{align*}	✓	✓	✓	✓	0.326
4923	20790	\begin{align*} x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.326
4924	24685	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=6 x^{2}-6 x -11 \\ \end{align*}	✓	✓	✓	✓	0.326
4925	25116	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=4 \\ \end{align*}	✓	✓	✓	✓	0.326
4926	25627	\begin{align*} y^{\prime \prime }+16 y&=0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.326
4927	456	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.327
4928	3147	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.327
4929	3209	\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }-2 y&={\mathrm e}^{x} x^{2} \\ \end{align*}	✓	✓	✓	✓	0.327
4930	14097	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.327
4931	17677	\begin{align*} x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 y^{\prime } x +4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.327
4932	18334	\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }&=\cos \left (x \right ) \cot \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.327
4933	18918	\begin{align*} y_{1}^{\prime }&=-y_{1}-5 y_{2}+3 \\ y_{2}^{\prime }&=y_{1}+3 y_{2}+5 \cos \left (t \right ) \\ \end{align*} With initial conditions \begin{align*} y_{1} \left (0\right ) &= 1 \\ y_{2} \left (0\right ) &= -1 \\ \end{align*}	✓	✓	✓	✓	0.327
4934	19655	\begin{align*} x^{\prime }&=-4 x-y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.327
4935	24460	\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=0 \\ y \left (0\right ) &= 2 \\ y \left (2\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.327
4936	24537	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=27 x^{2} \\ \end{align*}	✓	✓	✓	✓	0.327
4937	25968	\begin{align*} y^{\prime \prime }-y^{\prime }+y&=x^{3}-2 x^{2}+1 \\ \end{align*}	✓	✓	✓	✓	0.327
4938	1066	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.328
4939	1375	\begin{align*} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ y \left (0\right ) &= -3 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.328
4940	4128	\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=1 \\ \end{align*}	✓	✓	✓	✓	0.328
4941	6648	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=\left (-x^{2}+2\right ) {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.328
4942	6781	\begin{align*} {\mathrm e}^{x} y+4 \,{\mathrm e}^{x} y^{\prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+\left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.328
4943	7267	\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.328
4944	24474	\begin{align*} y^{\prime \prime }-4 y^{\prime }+7 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.328
4945	24657	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=12 \,{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.328
4946	1	\begin{align*} y^{\prime }&=2 x +1 \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.329
4947	579	\begin{align*} x^{\prime }&=10 y \\ y^{\prime }&=-10 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 4 \\ \end{align*}	✓	✓	✓	✓	0.329
4948	622	\begin{align*} x_{1}^{\prime }&=2 x_{1}+3 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+x_{2} \\ \end{align*}	✓	✓	✓	✓	0.329
4949	1067	\begin{align*} \left (x^{2}+2\right ) y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.329
4950	1074	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.329
4951	2198	\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=12 \,{\mathrm e}^{-x}+9 \cos \left (2 x \right )-13 \sin \left (2 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.329
4952	3187	\begin{align*} 4 y+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.329
4953	8636	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=6 \,{\mathrm e}^{2 t -3} \\ y \left (\frac {3}{2}\right ) &= 4 \\ y^{\prime }\left (\frac {3}{2}\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.329
4954	8900	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.329
4955	11768	\begin{align*} x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4956	13186	\(\left [\begin {array}{ccc} 3 & -3 & 1 \\ 2 & -2 & 1 \\ 0 & 0 & 1 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.329
4957	18099	\begin{align*} 2 y^{\prime \prime }&=\frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }} \\ y \left (1\right ) &= \frac {\sqrt {2}}{5} \\ y^{\prime }\left (1\right ) &= \frac {\sqrt {2}}{2} \\ \end{align*}	✓	✓	✓	✓	0.329
4958	18428	\begin{align*} x^{\prime }&=8 y-x \\ y^{\prime }&=x+y \\ \end{align*}	✓	✓	✓	✓	0.329
4959	19244	\begin{align*} y^{\prime }&=\arcsin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.329
4960	19422	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=4 x \\ \end{align*}	✓	✓	✓	✓	0.329
4961	19970	\begin{align*} {y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 y^{2} y^{\prime } x&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4962	20850	\begin{align*} y^{\prime \prime }+5 y^{\prime }-6 y&=3 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.329
4963	21169	\begin{align*} t^{2} x^{\prime \prime }-2 x&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4964	25164	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=4 \cos \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.329
4965	25165	\begin{align*} y^{\prime \prime \prime \prime }-y&={\mathrm e}^{t}+{\mathrm e}^{-t} \\ \end{align*}	✓	✓	✓	✓	0.329
4966	25659	\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.329
4967	896	\begin{align*} 4 y+y^{\prime \prime }&=\cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.330
4968	1291	\begin{align*} y^{\prime \prime }+2 y^{\prime }+6 y&=0 \\ y \left (0\right ) &= 2 \\ y^{\prime }\left (0\right ) &= \alpha \\ \end{align*}	✓	✓	✓	✓	0.330
4969	6085	\begin{align*} \left (1-a \right ) a y-2 a x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.330
4970	6268	\begin{align*} -2 \left (1-x \right ) y+2 \left (-x +3\right ) x \left (x +1\right ) y^{\prime }+\left (1-x \right ) x \left (x +1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.330
4971	7371	\begin{align*} y-2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.330
4972	8561	\begin{align*} y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.330
4973	9317	\begin{align*} y^{\prime \prime }-y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.330
4974	10439	\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\ \end{align*}	✓	✓	✓	✗	0.330
4975	16802	\begin{align*} y^{\prime }&=\delta \left (-2+t \right )-\delta \left (t -4\right ) \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.330
4976	21211	\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=-2 x \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= a \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.330
4977	21519	\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=2 x^{3}+5 x^{2}-7 x +2 \\ \end{align*}	✓	✓	✓	✓	0.330
4978	22184	\begin{align*} y^{\prime \prime }+y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.330
4979	24712	\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime }&=x^{2}-2 x \\ \end{align*}	✓	✓	✓	✓	0.330
4980	25636	\begin{align*} y^{\prime }-a y&=t \\ y \left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.330
4981	1096	\begin{align*} y^{\prime \prime }-2 y^{\prime } x +2 \alpha y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.331
4982	6240	\begin{align*} -2 y+y^{\prime } x +x^{4} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
4983	7593	\begin{align*} 3 y^{\prime \prime }+11 y^{\prime }-7 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4984	8052	\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
4985	10551	\begin{align*} 3 x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (1+3 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
4986	11438	\begin{align*} x^{2} \left (y^{\prime }+y^{2}\right )+a \,x^{k}-b \left (b -1\right )&=0 \\ \end{align*}	✓	✓	✓	✗	0.331
4987	13158	\(\left [\begin {array}{ccc} 4 & -3 & 1 \\ 2 & -1 & 1 \\ 0 & 0 & 2 \end {array}\right ]\)	✓	N/A	N/A	N/A	0.331
4988	16594	\begin{align*} y^{\prime \prime }-3 y^{\prime }-10 y&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.331
4989	17734	\begin{align*} \left (1+t \right )^{2} y^{\prime \prime }-2 \left (1+t \right ) y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4990	18155	\begin{align*} y^{\prime \prime }+25 y&=\cos \left (5 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.331
4991	18247	\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=1+8 \cos \left (x \right )+{\mathrm e}^{2 x} \\ \end{align*}	✓	✓	✓	✓	0.331
4992	19555	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.331
4993	19556	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=6 \,{\mathrm e}^{5 x} \\ \end{align*}	✓	✓	✓	✓	0.331
4994	19629	\begin{align*} y^{\prime \prime } x +\left (3 x -1\right ) y^{\prime }-\left (9+4 x \right ) y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✗	0.331
4995	21486	\begin{align*} y^{\prime \prime }+2 y^{\prime }+4 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.331
4996	21715	\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{-t} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.331
4997	23481	\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }&=1 \\ \end{align*}	✓	✓	✓	✓	0.331
4998	25638	\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=1 \\ y \left (0\right ) &= 4 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.331
4999	25950	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=2 \,{\mathrm e}^{2 x}+3 \sin \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.331
5000	26044	\begin{align*} y^{\prime \prime }+y^{\prime } x +2 y x&=0 \\ \end{align*}	✓	✓	✓	✗	0.331